Why are so many A-level Further Mathematics students confused about the basis for the theory they are being taught? Why do we often find it so hard to convince even our better students that Further Maths is a worthwhile choice of subject? Surely we know that a student with a decent pass in FM stands out in applications as someone who is capable if higher level thinking, who is not afraid to take on a challenge, and who has done that and succeeded? That’s not even mentioning the specialist skills and knowledge they have developed over their two years. My own experience is that I started teaching Further Maths A-level in 1974 (yes, that does make me feel old!) I have always felt that when a student really understands this work it’s the most fulfilling not only for the student, but also for the teacher. In my online tutoring, though, I’m finding students are having to learn topics in a strange order, sometimes having to just take the basic facts from their teacher, with the promise - “we’ll prove that later, in the single maths course.” So why is this happening?

There are two ways of managing Further Maths:

1. Teach all the single maths content in year 12, and as soon as it is completed, start the coverage of Further Maths, then in year 13 teach the rest of the Further Maths revise everything and do some past papers.

2. Put the Further Mathematics students in with the single maths students for as many lessons as you can, start teaching the Further Maths material in their other lessons from the word go, and therefore complete half of each course in year 12, the rest in year 13.

Clearly, the second way saves money, around five teaching hours per week, for each of two year groups, so that’s ten hours a week, roughly 40% of a teacher’s salary, or £20,000, which is a lot to a school, especially one where finances are hard at the moment, i.e. all schools! The first option is an ideal, but if you can achieve it, it’s worth the effort and yields dividends in the long run. I was blessed to have a headmaster who believed in me when I first suggested we went this way, and we both recognised it would be expensive at first. The first aim was to increase numbers. We felt that was justifiable because there were enough talented students in the school who were only studying single maths, and only doing three A-levels. We believed that for a talented mathematician, doing Maths and Further Maths rolled into one, because they can do most of their work very quickly, if the teaching was clear and answered all of their questions. A number of other tactics were used. I gave the second set in year 11 to my best teacher. Students from the top set would virtually all choose maths anyway, but the number choosing to do so from the second set determined how many would be taking maths in all. I told him what I wanted and he delivered - numbers for A-level maths went up, and it became a ‘cool’ subject to choose. As Head of dept, I was never one to monopolise top sets, but just for once I took the top set from their year 9 to year 11. Apart from teaching them the material, my aim more than ever before was to get them to enjoy maths, so I spent time with them really selling my subject, and in the nicest possible way I had to sell me. If they believed in me they might also believe that Further Maths is a good choice. By the time they were in the sixth form, we had very full single maths sets and a double maths set of 12. That was enough, and we started teaching Further Maths according to method 1. Again, they had to succeed, so they got me best teachers, unashamedly. Others would get their turn later but this year group had to do well.

They didn’t disappoint. I think they knew they were getting special treatment and they responded. Most had two A grades (no A*s in those days) and news of their success spread to year 11 - and outside the school. External candidates began to apply to do double maths with us and the income we had because of that enabled us in one particular year to have two Further Maths sets for the Pure parts of the course.

That was over 20 years ago. I retired in 2015, but have been dropping in for a couple of mornings a week to help out over the last two years. The school now has two double maths sets as a fixture, attracts sixth formers in significant numbers and the maths department is as strong as any I have experienced, with some great teachers.

More than that, though, the students in year 12 finish all the single maths content before they tackle the Further Maths topics, which mostly depend on it. With less confusion, they progress more quickly and have time to answer all the awkward questions, even to consider some parts of maths that don’t make the exam course. (I once read a scheme of work which ended with “It is forbidden not to waste time”, which I thought was great.) So they are ready at the end of year 12 to hit the further Maths course feeling confident and eager, rather than confused and fearful.

If you’re currently using method 2, do think what it would take to make the change.

12/9/25